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The function sin^(2) (omegat) represent...

The function sin^(2) (omegat) represents.

A

a periodic motion, but not SHM with a period `2pi//omega`

B

a periodic motion, but not SHM with a period `pi//omega`

C

an SHM with a period `2pi//omega`

D

an SHM with a period `pi//omega`

Text Solution

Verified by Experts

The correct Answer is:
D
`x=sin^(2)omegatx=(1/2+x) ` where =`(1-cos2omegat)/2` implies `x = x=1/2-1/2cos 2omegatimpliesx=1/2cos(2omega+pi)``implies` period, T=`2pi//2omega`=`x//omega ` So the given function is an SHM with mean position at ` x=0(x=1/2)`,amplitude `1/2 `and time period `2pi//2omega=pi//omega`
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